Do RNNs/LSTMs really need to be sequential?
You are talking about model parallelism. But, that's not the reason RNNs/LSTMs are not in vogue.
Imagine your ability to read the first line of a page and going on reading and still making connections to the first line until the end of the page.
Can RNNs/LSTMs do that? No.
Can Attention (i.e. Transformers) do it? Yes.
The reason is simple Attention is effectively an affinity matrix between each and every input that goes into a network. So, it is able to do that. We have a huge memory overload but hey, we want the performance.
In case of RNNs/LSTMs, the cells have to do this heavy-lifting, there is only a set amount of information that can be contained in them. That's why you have to forget gate to control information retained.
Nevertheless, your thought is correct but that's not the reason for Attention to be in vogue. But, your thought has negative ramifications when we see how to implement it. Also, nevertheless the computation will be still sequential since you can't process input (n + 1) without input n. Local parallelization is possible but not global.